随机逻辑斯谛过程中的灭绝时间与矩闭合

Extinction times and moment closure in the stochastic logistic process.

作者信息

Newman T J, Ferdy Jean-Baptiste, Quince C

机构信息

Department of Physics and Astronomy, Arizona State University, P.O. Box 871504, Tempe, AZ 85287, USA.

出版信息

Theor Popul Biol. 2004 Mar;65(2):115-26. doi: 10.1016/j.tpb.2003.10.003.

DOI:10.1016/j.tpb.2003.10.003

PMID:14766186

Abstract

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4 / M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.

摘要

我们研究了一个孤立种群灭绝时间的统计数据，该种群最初个体数量为适度的(M)，其动态由随机逻辑斯蒂过程（SLP）控制。当死亡率和出生率的值接近时，发现灭绝时间(V)的变异系数有最大值。对于大的栖息地规模(K)，我们发现(V_{max})的量级为(K^{1/4} / M^{1/2})，只要(M)比(K^{1/2})小得多，这个值就远大于(1)。我们还使用矩封闭近似（MCA）对SLP进行了研究，并讨论了该方法的成功与失败之处。关于前者，当死亡率较低时，MCA产生了种群的稳态分布。尽管对于SLP模型来说并不正确，但该分布的前三个矩与为禁止灭绝的调整后的SLP精确计算出的矩一致。这些精确计算也指出了随着死亡率增加MCA的失效。